Video Transcript
Determine the length of line
segment 𝐴𝐷.
We note that 𝐷 is the projection
of 𝐴 onto the line 𝐵𝐶 and that the triangle 𝐴𝐵𝐶 is a right triangle at 𝐴. And we recall that the corollary to
the Euclidean theorem, that is, the altitude rule, tells us that 𝐴𝐷 squared is
equal to 𝐵𝐷 multiplied by 𝐶𝐷. This tells us that the altitude or
height of the right triangle squared is the product of the lengths of the segments
of the hypotenuse when it is split by the altitude.
We’re given that the two segments
are 2.5 centimeters, that’s 𝐶𝐷, and 6.4 centimeters, that’s 𝐵𝐷. And substituting these values in,
we have 𝐴𝐷 squared is 6.4 multiplied by 2.5. This evaluates to 16, so 𝐴𝐷
squared is 16. Now, taking the square root on both
sides of the equation, noting that 𝐴𝐷 is a length and so is nonnegative, we get
𝐴𝐷 is the square root of 16, which is four. The length of 𝐴𝐷 is therefore
four centimeters.
